Use a calculator to verify that Σx = 133, Σx2 = 6837, Σy = 148, Σy2 = 4674, and Σxy = 3004. Compute r. (Round your answer to three decimal places.)
I wonder if a set of data is missing.
This the data missing:
Do larger universities tend to have more property crime? University crime statistics are affected by a variety of factors. The surrounding community, accessibility given to outside visitors, and many other factors influence crime rate. Let x be a variable that represents student enrollment (in thousands) on a university campus, and let y be a variable that represents the number of burglaries in a year on the university campus. A random sample of n = 8 universities in California gave the following information about enrollments and annual burglary incidents.
x 12.1 30.4 24.5 14.3 7.5 27.7 16.2 20.1
y 24 68 39 23 15 30 15 25
To compute the correlation coefficient (r), we can use the following formula:
r = (Σxy - (Σx * Σy) / n) / √((Σx^2 - (Σx)^2 / n) * (Σy^2 - (Σy)^2 / n))
Given values:
Σx = 133
Σx^2 = 6837
Σy = 148
Σy^2 = 4674
Σxy = 3004
Now, let's compute r step-by-step:
Step 1: Calculate n, the number of data points.
n = √(Σx^2 - (Σx)^2 / n)
= √(6837 - (133)^2 / n)
= √(6837 - 17689 / n)
= √(6837 - 132.3942308)
= √(6704.6057692)
= 81.8890396
Step 2: Calculate the numerator of the r formula.
Numerator = Σxy - (Σx * Σy) / n
= 3004 - (133 * 148) / 81.8890396
= 3004 - 19684 / 81.8890396
= 3004 - 240.0779489
= 2763.922051
Step 3: Calculate the denominator of the r formula.
Denominator = √((Σx^2 - (Σx)^2 / n) * (Σy^2 - (Σy)^2 / n))
= √((6837 - (133)^2 / n) * (4674 - (148)^2 / n))
= √((6837 - 17689 / n) * (4674 - 21904 / n))
= √((6837 - 132.3942308) * (4674 - 2373.3942308))
= √((6704.6057692) * (2300.6057692))
= √(15423415.014183)
= 3929.694498
Step 4: Calculate r using the numerator and denominator.
r = Numerator / Denominator
= 2763.922051 / 3929.694498
= 0.703615
Therefore, r is approximately 0.704 (rounded to three decimal places).
To compute the correlation coefficient (r) using the given information, we can use the following formula:
r = (Σxy - (Σx * Σy) / n) / √((Σx2 - (Σx)² / n) * (Σy2 - (Σy)² / n))
where:
Σxy represents the sum of the product of x and y values,
Σx represents the sum of all x values,
Σy represents the sum of all y values,
Σx2 represents the sum of the squares of x values,
Σy2 represents the sum of the squares of y values, and
n represents the total number of data points.
Let's substitute the given values into the formula:
Σx = 133
Σx2 = 6837
Σy = 148
Σy2 = 4674
Σxy = 3004
n = ? (we need this information to compute the correlation coefficient)
Since the total number of data points (n) is not provided, we cannot compute the correlation coefficient (r) without this information. Please provide the total number of data points, and I will be happy to help you calculate the correlation coefficient.